Sigma-delta digital-to-analog converters ("DACs") and analog-to-digital converters ("ADCs") recently have come into widespread use with the development of suitable process technology and the increase in digital audio and other applications. Sigma-delta converters utilize oversampling techniques (i.e., sampling at rates greater than the Nyquist rate) to achieve high signal-to-noise ratios. Such converters also exhibit excellent linearity. Additionally, sigma-delta converters are relatively straight-forward and inexpensive to implement due to their simplicity.
Sigma-delta DACs commonly include a front-end interpolator which receives digital input samples and increases the sampling rate (typically 64 times the input sample rate) of the digital input samples. A sigma-delta modulator receives the higher frequency input samples from the interpolator and converts the samples to a lower accuracy (typical one-bit), high frequency bit stream. Additionally, the sigma-delta modulator performs an oversampling technique referred to as "noise shaping". "Noise shaping" is a technique by which the noise spectrum of the input samples is manipulated such that a major component of the quantization noise power is shifted to a frequency range higher than the upper frequency limit of the band of interest, which is typically the signal bandwidth. The one-bit data stream output by the modulator is converted to an analog signal by a conventional DAC and subsequent filtering is performed in the analog domain to reduce the high frequency quantization noise component of the analog output signal. Sigma-delta converters are described in Mixed-Signal Design Seminar, published by Analog Devices, Inc., Norwood, Mass., 1991, which reference is incorporated herein by reference.
FIG. 1 is a block diagram showing a typical one-bit prior art sigma-delta DAC system. The system includes an up-sample interpolator element 12, a digital low pass filter 16, a sigma-delta modulator 20, a one-bit DAC 24 and an analog low pass filter 28. Digital input samples are received on n-bit input bus 10 and provided to up-sample element 12. The digital input samples can be any number n of bits and can have any input sample rate. For example, a typical compact disc player application includes 16-bit digital input samples having an input sample rate of 44.1 kHz. Up-sample element 12 increases the input sample rate of the digital input samples by a factor of Z, typically 64. Z is referred to as an "interpolation ratio" or "up-sampling factor". The up-sampled digital input samples are provided on n-bit bus 14 to digital low pass filter 16 which filters the up-sampled digital input samples. Filter 16 filters out images between a baseband frequency and the up-sampled sampling rate. Those skilled in the art will understand that while up-sample element 12 and low pass filter 16 are shown as separate elements, those elements typically are practically implemented with a single element interpolation filter.
The filtered digital samples are provided on n-bit bus 18 to sigma-delta modulator 20. Sigma-delta modulator 20 modulates the received digital samples at an "oversampling rate" (equal to the up-sampled rate of the digital samples) and outputs a one-bit digital stream on one-bit bus 22. While the sigma-delta modulator 20 is shown and described herein as a one-bit modulator, those skilled in the art will appreciate that modulators greater than one-bit are available and are used depending on accuracy requirements. The sigma-delta modulator 20 conventionally performs noise-shaping on the digital samples providing a one-bit output stream essentially having a low-frequency signal component and a high-frequency quantization noise component.
The one-bit data stream is provided on bus 22 to one-bit DAC 24 which conventionally converts the data stream into an analog output signal on line 26. The analog output signal is provided on line 26 to low pass filter 28 which conventionally reduces the high frequency quantization noise component of the signal. As will be understood by those skilled in the art, low pass filter 28 does not actually eliminate the quantization noise, but simply reduces it to acceptable levels to suit a particular application (i.e., so that the signal can subsequently be handled by other components such as loudspeakers, etc.). Complete elimination of the quantization noise is not necessary, for example, in a compact disc player application, because the quantization noise substantially resides within an inaudible frequency range, above the audible range (i.e., above 20 kHz).
A limitation of conventional DACs, including the typical sigma-delta DAC shown in FIG. 1, is that they determine the magnitude of the input samples only at equally spaced temporal intervals. Such a process is known as uniform sampling. Additionally, with conventional DACs, the digital input sample rate is not made independent of the master clock signal used for clocking the sigma delta modulator. The input sample rate must be some integer division of the master clock signal. Consequently, if an application requires two different digital input sample rates, at least one of which is not divisible into the master clock signal, for example, then two master clock signals (having different frequencies) are required for clocking the sigma-delta modulator.
Accordingly, a general object of the present invention is to provide a method and apparatus for performing digital-to-analog conversion using non-uniform sampling (i.e., variable temporal spacing of the sampling points, independent of the master clock signal).